Precise measurements give the following masses:nuclide mass11H 1.0078u42He 4.00260uparticle mass10n 1.0086649u0−1e ×5.485810−4u01e ×5.485810−4uNow consider the following nuclear reaction:→+211H 210n 42HeIs energy released or absorbed by this reaction? releasedabsorbedneither releasednor absorbedI need moreinformation to decide.If you said energy was released or absorbed, calculate how much energy is released or absorbed.kJ/molGive your answer in both kJ/mol and MeV. Be sure each of your answer entries has the correct number of significant digits.Note: take particular care to keep enough digits in any intermediate calculation, and use enough digits in any scientific constants you need, since the data with which you are working are very precise. MeV
Question
Precise measurements give the following masses:nuclide mass11H 1.0078u42He 4.00260uparticle mass10n 1.0086649u0−1e ×5.485810−4u01e ×5.485810−4uNow consider the following nuclear reaction:→+211H 210n 42HeIs energy released or absorbed by this reaction? releasedabsorbedneither releasednor absorbedI need moreinformation to decide.If you said energy was released or absorbed, calculate how much energy is released or absorbed.kJ/molGive your answer in both kJ/mol and MeV. Be sure each of your answer entries has the correct number of significant digits.Note: take particular care to keep enough digits in any intermediate calculation, and use enough digits in any scientific constants you need, since the data with which you are working are very precise. MeV
Solution
To determine whether energy is released or absorbed in a nuclear reaction, we need to calculate the difference in mass before and after the reaction. This is based on Einstein's equation E=mc^2, which states that mass and energy are interchangeable.
The mass before the reaction is the sum of the masses of two hydrogen atoms (2 * 1.0078 u) and one neutron (1.0086649 u). The mass after the reaction is the mass of the helium atom (4.00260 u).
Mass before the reaction = 2 * 1.0078 u + 1.0086649 u = 3.0242649 u Mass after the reaction = 4.00260 u
The difference in mass (Δm) is the mass before the reaction minus the mass after the reaction.
Δm = 3.0242649 u - 4.00260 u = -0.9783351 u
The negative sign indicates that mass is lost in the reaction, which means energy is released.
To calculate the amount of energy released, we use Einstein's equation E=mc^2. However, we need to convert the mass difference from atomic mass units (u) to kilograms (kg) and use the speed of light in meters per second (m/s). The conversion factors are 1 u = 1.66053906660 × 10^-27 kg and c = 2.99792458 × 10^8 m/s.
Δm = -0.9783351 u * 1.66053906660 × 10^-27 kg/u = -1.625 × 10^-27 kg
E = Δm * c^2 = -1.625 × 10^-27 kg * (2.99792458 × 10^8 m/s)^2 = -1.46 × 10^-12 Joules
To convert this to kilojoules per mole (kJ/mol), we use the conversion factors 1 J = 1 × 10^-3 kJ and 1 mol = 6.02214076 × 10^23 entities.
E = -1.46 × 10^-12 J * 1 × 10^-3 kJ/J * 1 mol/6.02214076 × 10^23 entities = -2.42 × 10^-13 kJ/mol
To convert this to Mega electronvolts (MeV), we use the conversion factor 1 J = 6.242 × 10^12 MeV.
E = -1.46 × 10^-12 J * 6.242 × 10^12 MeV/J = -9.11 MeV
So, the energy released by the reaction is 2.42 × 10^-13 kJ/mol or -9.11 MeV.
Similar Questions
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